Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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3answers
219 views

Diameter of wheel

If a wheel travels 1 mile in 1 minute at a rate of 600 revolutions per minute. What is the diameter of the wheel in feet ? The answer to this question is 2.8 feet. Could someone please ...
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3answers
9k views

How to prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact?

I've tried drawing a parallel chord to the tangent but then how would you prove that the chord is perpendicular to the radius?
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2answers
468 views

circles and linear fractional transformations

I'm realizing how little (in some respects) I know about circles. Here's something that emerged out of something I was fiddling with. My question is whether this is "well known" in the way that ...
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1answer
141 views

Can't understand this solution.

I came across a problem which was already present on the internet. If an arc with a length of $12\pi$ is $\frac{3}{4}$ of the circumference of the circle, what is the shortest distance between ...
3
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2answers
281 views

Angles of triangle inside a cricle

In the figure shown if area of circle with center o is 100pi and CA has length of 6 what is length of AB ? I looked around on the web and cant seem to get an idea of what the angles AOC ...
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1answer
117 views

rather simple question

This is probably an easy question but I don't get it. Please answer in a easy way :P Imagine you want to paint circles on a linear line. The line is 100cm long. On the right side you have a circle ...
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4answers
2k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
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2answers
61 views

rates of motion of projected points along a circle

Have I forgotten all my secondary-school geometry? (That's not actually my question.) Suppose $R>r>0$ and consider this circle (later edit: I think $R>0$, $r>0$ is enough; we don't ...
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1answer
603 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
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1answer
700 views

Finding points relating to the edge of a circle in an x,y coordinate system

My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
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1answer
246 views

Find a circle that is tangent to a line and a circle.

I need to find the circle that will be tangent to a line at a given point and a circle. The diagram below hopefully makes it clearer. The known data are: points P2,P3,P4,P5 Circle C2's radius r ...
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2answers
416 views

Connecting two tangents with two circles of equal radius

In a cartesian system I have 2 lines (an input and an output) and want to find the radius (r) and centre (c1, c2) of the two circles of equal radius that are touched tangentially at the end point of ...
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1answer
250 views

Rotation $x \to x+a \pmod 1$ of the circle is Ergodic if and only if $a$ is irrational

I have a book, Ergodic problems of classical mechanics by Arnold/Avez, and in it they prove that rotation $Tx = x+a \pmod 1$ of the circle $M=\{x \pmod 1\}$ is Ergodic if and only if a is irrational. ...
2
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3answers
787 views

3-D equation of a circle

I came across a sum but could not solve it as i dont know the 3d equations of a circle : The sum is If $A(3,-2,2)$ and $B(2,9,5)$ are the end points of a diameter of a circle,then the third pt that ...
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3answers
641 views

angle of an inscribed triangle

I have a scalene triangle inscribed in a circle, one of its sides $a$ is $2\sqrt3$ and the length $r$ from that side to the center is $1$. I need to find the angle $x$ opposite to the side given. ...
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1answer
834 views

How to turn this sum into an integral?

I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
2
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1answer
268 views

Convergence and closed form of this infinite series?

If we have a circle of radius $r$ with an $n$-gon inscribed within this circle (i.e. with the same circumradius), we can find the difference of the areas using: $$A_n =\overbrace{\pi r^2}^\text{Area ...
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3answers
2k views

Average distance between two points in a circular disk

How can I find an average distance between two points lying inside a circular disk of a certain radius? I wonder if there is any other way except of using a Monte Carlo method?
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5answers
3k views

Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator?

Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator? $150$ degree the right answer are $\frac{1}{2}$, $-\frac{\sqrt{3}}{2}$and $-\frac{1}{\sqrt{3}} $ $-315$ degree the ...
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1answer
266 views

Finding the measure of $\angle AEB$ given a figure

In the given figure, $O$ is the center of the circle and $$ \angle AOB =120$$ How could I find the measure of $\angle AEB$? Thanks in advance.
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2answers
521 views

Find the radius of the circle?

Three circles of equal radii have been drawn inside an equilateral triangle , of side a , such that each circle touches the other two circles as well as two sides of triangle. Then find the radius ...
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2answers
12k views

Distance Between Any Two Points on a Unit Circle

As part of a larger investigation, I am required to be able to calculate the distance between any two points on a unit circle. I have tried to use cosine law but I can't determine any specific manner ...
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1answer
4k views

How does this equation to find the radius from 3 points actually work?

I had searched online and found an equation that solves the radius of a circle from 3 points that are located on the circumference of that specific circle. Where I had found this formula did not state ...
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1answer
186 views

How to find the area. Linked with another question. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? In this question we discussed why the fake proof is wrong. But, what about the area? The process converges to the same area of the circle ...
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1answer
717 views

internally and externally tangent circles

See the diagram here: diagram The diagram shows two circles of radius 1 and 2 tangent to each other and internally tangent to a circle of radius 3. What is the radius of the outlined circle ...
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0answers
154 views

Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum

I want the calculate the "value" of an angle in such a way that: The angle of 45 degrees corresponds with the maximum value of 1 The angles of 0 and 90 degrees correspond with the minimum value of 0 ...
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1answer
368 views

Meaning of this 4x4 determinant

Let $p,q,r$ and $s$ be four points on the plane. Moreover, $p,q,r$ are given in clockwise order. My book said that the following determinant is positive if and only if $s$ lies inside the circle ...
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1answer
188 views

Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
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2answers
216 views

Find the ratio in which the circle divides each of the sides AB and AC?

A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint . Find the ratio in which the circle divides each of the sides AB and AC? Does the line ...
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4answers
379 views

What is the radius of the circle in cm?

The rectangle at the corner measures 10 cm * 20 cm. The right bottom corner of the rectangle is also a point on the circumference of the circle. What is the ...
1
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3answers
1k views

Find the radius of the circle?

Two Circle of an equal of an radii are drawn , without any overlap , in a semicircle of radius 2 cm. If these are the largest possible circles that the semicircle can accomodate , then what is the ...
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1answer
2k views

Closest point on circle edge from point outside/inside the circle

Alright, I am programming a plugin for a game that requires me to get the closest point on a circle when all you have is a point B, which is outside of the circle, the radius of the circle, and the ...
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3answers
3k views

Find the length of the common chord

"Two circles with centres C1 and C2 and radius 6 cm and 8 cm respetively cut each other at right angles. Find the length of the ...
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1answer
3k views

Integer solutions (lattice points) to arbitrary circles

Wolfram Alpha will provide integer solutions to arbitrary circle equations. I'm trying to understand how it's able to calculate them, but despite a fair bit of digging I haven't found any discussion ...
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0answers
102 views

contradicting PI=4 fallacy. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? I know that you can take area out of a square without changing it's perimeter. Now, here's this problem: Draw a circle with dia = 1; Draw a ...
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1answer
70 views

Computing angle

See the drawing for the situation. Given lenghts a, b and c and also L, but k and angle alpha are unknown. How to compute this angle alpha? I know it is possible to compute if we first compute k in ...
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2answers
429 views

Given an angle, get the trigonometric circle point.

Given an angle, in degrees, how can I get the trigonometric circle point coordinates for it? For instance, given the angle 0, I would get (1,0). 90 would be (0,-1). Clockwise.
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2answers
1k views

Calculate radius of variable circles surrounding big circle.

I got a circle, which I know all the details about him. (Radius [100], Diameter [200], Circumference [628.32], Area [31415.93]...) I would like to surround this circle, with smaller circles. I know ...
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1answer
881 views

Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
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1answer
130 views

Function for the upper left part of a circle

What is the function corresponding to the upper left quarter of a circle ? Where $x$ goes from 0 to $x_\text{max}$, and $y=f(x)$ goes from $y_\text{min}$ to $y_\text{max}$.
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1answer
125 views

Circle : How to get all co-ordinate list of circle parimeter?

I want to find all the co-ordinate of circle. I know the radius of circle and considering center co-ordinate as (0,0). So Is there any equation for finding all ...
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1answer
541 views

Tough Geometry Problem--Regular Polygon inside Circle

$ABCDEFG$ is a regular heptagon inscribed in a unit circle centered at $O$. $\ell$ is the line tangent to the circumcircle of $ABCDEFG$ at $A$, and $P$ is a point on $\ell$ such that triangle $AOP$ is ...
3
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0answers
555 views

Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
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1answer
693 views

How do you find the angle of circle segment formed with points (x,y) and (radius,0)?

I've been learning about the unit circle, sine, cosine, and the like in my introduction to trigonometry course, but I'm drawing a blank here. If I have a circle centered at the origin, with radius r ...
3
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1answer
2k views

Packing squares into a circle

I need determine the maximum number of squares of the given size that can be packed into a circle of the given radius. Squares can be rotated. I'm not sure how complex this problem is and i can find ...
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4answers
2k views

I need a proof that a line cannot intersect a circle at three distinct points

I need a simple proof that a line cannot intersect a circle at three distinct points.
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1answer
379 views

equation to get 10 points on circle surface at fix distance

What I tried is : $$x = \sin(36 \cdot 50 \cdot 3.14)/180$$ $$y = \cos(36 \cdot 50 \cdot 3.14)/180$$ Here $36$ is because I want 10 points on circle so $360/10=36$. $50$ is center X and center Y ...
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2answers
220 views

Area of a circle

I've tried to find as a personnal exercise where the formula $A=\pi R^2$ comes from. After drawing the problem, I've found that $A = 2\int\limits_{-R}^{R}\sqrt{R^2-t^2}dt$. How can I calculate this ? ...
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0answers
250 views

What “boundary conditions” can make a rectangle “look” like a circle?

I posted the question below in Stackoverflow but then realized that it perhaps would find a better audience here. I am solving a fourth order non-linear partial ...
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4answers
3k views

How to calculate the two tangent points to a circle with radius R from two lines given by three points

I need to calculate the two tangent points of a circle with the radius $r$ and two lines given by three points $Q(x_0,y_0)$, $P(x_1,y_1)$ and $R(x_2,y_2)$. Sketch would explain the problem more. I ...